| Title:
|
The axioms for implication in orthologic (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
15-21 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice. (English) |
| Keyword:
|
ortholattice |
| Keyword:
|
orthoimplication |
| Keyword:
|
orthologic |
| MSC:
|
03G12 |
| MSC:
|
03G25 |
| MSC:
|
06C15 |
| idZBL:
|
Zbl 1174.06310 |
| idMR:
|
MR2402523 |
| . |
| Date available:
|
2009-09-24T11:53:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128243 |
| . |
| Reference:
|
[1] J. C. Abbott: Semi-boolean algebra.Matematički Vesnik 4 (1967), 177–198. Zbl 0153.02704, MR 0239957 |
| Reference:
|
[2] J. C. Abbott: Orthoimplication algebras.Studia Logica 35 (1976), 173–177. Zbl 0331.02036, MR 0441794, 10.1007/BF02120879 |
| Reference:
|
[3] I. Chajda, R. Halaš and H. Länger: Orthomodular implication algebras.Intern. J. of Theor. Phys. 40 (2001), 1875–1884. MR 1860644, 10.1023/A:1011933018776 |
| Reference:
|
[4] I. Chajda, R. Halaš and H. Länger: Simple axioms for orthomodular implication algebras.Intern. J. of Theor. Phys. 43 (2004), 911–914. MR 2106354, 10.1023/B:IJTP.0000048587.50827.93 |
| Reference:
|
[5] I. Chajda, G. Eigenthaler and H. Länger: Congruence Classes in Universal Algebra.Heldermann Verlag, 2003. MR 1985832 |
| Reference:
|
[6] B. Jónsson: Algebras whose congruence lattices are distributive.Math. Scand. 21 (1967), 110–121. MR 0237402, 10.7146/math.scand.a-10850 |
| Reference:
|
[7] G. Kalmbach: Orthomodular Lattices.Academic Press, London, 1983. Zbl 0528.06012, MR 0716496 |
| . |
